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arXiv · 2512.05652

On moments of the Erd\H{o}s--Hooley Delta-function

R. de la Bretèche·G. Tenenbaum
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Abstract

For integer $n\geqslant 1$ and real $u$, let $\Delta(n,u):=|\{d:d\mid n,\,{\rm e}^u<d\leqslant {\rm e}^{u+1}\}|$. The Erd\H{o}s--Hooley Delta-function is then defined by $\Delta(n):=\max_{u\in{\mathbb R}}\Delta(n,u).$ We provide new upper bounds for weighted real moments of this function.

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R. de la Bretèche, G. Tenenbaum. 2025-12-05. On moments of the Erd\H{o}s--Hooley Delta-function. https://arxiv.org/abs/2512.05652

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